By Sameer Chavan, IIT Kanpur

Abstract 

For a hyponormal operator, that is, an operator with a positive self-commutator, Putnam’s inequality provides an upper bound for the norm of its self-commutator. In the special case of a Toeplitz operator with an analytic symbol in the Smirnov class of a domain, Khavinson established a geometric lower bound. When combined with Putnam’s inequality, this lower bound yields the classical isoperimetric inequality. In the second half of the talk, we will discuss multivariable counterparts of Putnam’s inequality and explore some of their consequences.